How many complex numbers are there where and are integers and
Details and assumptions:
denotes the modulus or absolute value.
Given that are complex numbers that satisfy the system of equations above and that equals for coprime positive integers , evaluate .
Let and .
Let be a complex number such that , and =.
Find
Details and Assumptions:
Let be a solution to the equation .
Find the value of
Let and be the two complex roots of the equation , where and are real numbers. Further, assume that the origin, and form an equilateral triangle. Then: